Why not read a bunch of books instead?
If the point is to become a well rounded person, think widely and read widely, then getting a PhD isn't going to help you much. I think of PhD's as very driven, focused, able to take a lot of abuse, able to write and research for several years. I don't think of them as particularly well rounded.
In particular, getting a PhD in Philosophy from Stanford after a BS in CS from Columbia and an MS from MIT is going to give you a couple of survey courses in Philosophy, and then a very deep knowledge of a very, very narrow band of philosophy..
I learned how the quantifiable, individualistic, ahistorical—that is, computational—view I had of cognition failed to account for whole expanses of cognitive experience (including, say, most of Shakespeare). I learned how pragmatist and contextualist perspectives better reflect the diversity and flexibility of our linguistic practices than do formal language models.
QED.
If the point is to be well read, well rounded, and be able to think broadly about a variety of topics, then... read a book. Read a lot of books. Read broadly. Read widely. Read people that you disagree with. Argue with writers.
Read literature, comparative religions, philosophy, cultural anthropology, sociology, history, science fiction, mythology, fantasy, psychology, biography, poetry.
Read Carl Jung, Freud, Neitsche, Marx, Kant, Dickenson, Poe, Emerson, Hawthorne, Plato, Aristotle, the Bhagvad Gita, the Koran, the Tao, The Tao of Poo, Luther, Martin Luther King, Tolstoy and Doestoyevsky, Adams, St. John of the Cross, the Mystics--Christian, Bhuddist, Kabbalist, and Sufi, Gleick, Feynman, Shakespeare, Chaucer.
Chances are, if they say it's a "classic" it's probably hung around for a long time because it's good. (Except for Kant. He couldn't write worth crap). And, in reading we learn that we are not alone. We learn that perhaps creating a True AI isn't something to be desired anyway. We learn that maybe consciousness is more than a deterministic bunch of bio-chemical reactions taking place in our frontal lobes that can be modeled via neural networks and computer processors. And, we start to wonder, if perhaps as the poets proclaim... there something called a Soul. And if there is a Soul, can we actually create that via silicon, light, magnetics and electricity?
You can get that education in $1.50 in late charges at the library. You don't have to spend 3 years and $150k at Stanford working on your Phd.